It's the 64 thousand dollar question!! I think the answer is, at whatever age they let you!
If you look down the page, I posted a question "wrapped to unwrapped". I have a 4 month old who needs to be wrapped to sleep, but doesn't want to be. She really puts on a temper tantrum at being put into bed wrapped, but if I loosen the wrap and let her get her hands out, 10minutes later I'm back trying to settle her because her arms are flaying about and she is upset!! She really turned it on last night and I tried different ways of wrapping, leaving the wrap loose, forgetting the wrap all together. She was awake every 2 hours. Eventually I got tired of it all and I wrapped her up tight and she slept for 4hrs straight, woke up had a bottle and I put her back to bed wrapped again and she is going on for 4hrs again, when she normally only sleeps for an 1hr after her morning bottle.
If you can put bub's to bed without being wrapped and they are sleeping ok, then forget the wrap and lucky you! A friend of mine still wrapps her boy and he is 12months old. Good luck!
Angie, DE 15/12/05 ,TAS